I don't know which places deliver, which can vary from one location to another. But I can tell you where to go for great Chicago-style deep-dish pizza in the vicinity of your hotel, for the double-crust "stuffed" style as well as the single-crust "pan" style. You can look up their number and call them to ask about delivery.

I'm sure you're aware that the pizza is likely to be hotter and better at the restaurant, hot out of the oven, than by getting it delivered. Here are a couple more tips for you. If you eat at the restaurant, you can phone ahead with your pizza order to avoid waiting 30-45 minutes while seated for your pizza to bake. And if you're getting the pizza delivered, they may ask you whether or not you want it cut/sliced; cutting/slicing it may leave it a bit soggy by the time it gets delivered, whereas leaving it uncut keeps the crust crisper (but obviously you would then need to scrounge up a knife with which to cut it - hopefully the delivery includes plasticware which you can use).

Giordano's (in the Prudential building) and Bacino's are slightly closer than the others (4 blocks from the hotel vs about 6-8 blocks for the others). Giordano's is also my personal favorite, but all of these are delicious.